does this even make sense?

Top off the brake fluid and see if it still happens.

Yes, it makes no immediate sense, but the HIDs would have a substantial current draw. That could lower the voltage of the system, which could have an effect on resistance type sensors. Just give it a try and report back.

Well, if this isn't a straight plug and play HID kit, it may have a weak resistor or relay that isn't functioning completely. If it is, it might be low brake fluid or a dirty ABS sensor. Any other work done? Or muddy/dirty traveling recently either?

As bhuff said, HIDs can draw a significant current (though they only do so for a very short period of time when power is first applied; in steady-state, once lit-off, HIDs actually draw less current than halogens...)

However, HIDs don't just suffer from a high "inrush" current, they also can produce a significant amount of what's known as "EMI" or "electromagnetic interference." This is because inside the HID is a power supply that boosts the car's 12V system voltage to a much higher level needed to start and maintain the HID bulbs. These power supplies, if not designed well, can generate significant EMI both radiated (which can sometimes be heard as crackling in the radio speakers when tuned to an AM radio station) and conducted (which can play hell with sensitive electronics in the rest of the car by contaminating the 12V source...)

Double-check your installation. Make sure you've got good quality grounds. If the case of the ballast needs to be grounded, make sure it is. Use a relay drawing power from the battery (through a proper fuse, obviously) to run the HIDs and trigger the relay coil using the car's OE headlight wiring.

What brand are the HIDs? Cheap off-shore crap or quality parts?